Associative Property of Addition - Definition & Worksheets - Free Printable

Problem: Solve the missing numbers using the Associative Property of Addition.

The Associative Property of Addition states that when adding three or more numbers, the way in which the numbers are grouped does not affect the sum. Mathematically, this is expressed as:
\[
(a + b) + c = a + (b + c)
\]

We will use this property to solve each problem step by step.

---

Problem 1:

\[
(33 + \_\_) + 15 = 33 + (21 + 15)
\]

#### Step 1: Simplify the right-hand side.
\[
33 + (21 + 15) = 33 + 36 = 69
\]

#### Step 2: Set up the left-hand side.
\[
(33 + \_\_) + 15 = 69
\]

#### Step 3: Let the missing number be \( x \).
\[
(33 + x) + 15 = 69
\]

#### Step 4: Simplify the left-hand side.
\[
33 + x + 15 = 69
\]
\[
48 + x = 69
\]

#### Step 5: Solve for \( x \).
\[
x = 69 - 48
\]
\[
x = 21
\]

#### Final Answer:
\[
\boxed{21}
\]

---

Problem 2:

\[
\_ + (9 + 2) = (17 + 9) + 2
\]

#### Step 1: Simplify the right-hand side.
\[
(17 + 9) + 2 = 26 + 2 = 28
\]

#### Step 2: Set up the left-hand side.
\[
\_ + (9 + 2) = 28
\]

#### Step 3: Simplify \( 9 + 2 \).
\[
9 + 2 = 11
\]
So the equation becomes:
\[
\_ + 11 = 28
\]

#### Step 4: Let the missing number be \( y \).
\[
y + 11 = 28
\]

#### Step 5: Solve for \( y \).
\[
y = 28 - 11
\]
\[
y = 17
\]

#### Final Answer:
\[
\boxed{17}
\]

---

Problem 3:

\[
154 + (\_ + 30) = (154 + 48) + 30
\]

#### Step 1: Simplify the right-hand side.
\[
(154 + 48) + 30 = 202 + 30 = 232
\]

#### Step 2: Set up the left-hand side.
\[
154 + (\_ + 30) = 232
\]

#### Step 3: Let the missing number be \( z \).
\[
154 + (z + 30) = 232
\]

#### Step 4: Simplify the left-hand side.
\[
154 + z + 30 = 232
\]
\[
184 + z = 232
\]

#### Step 5: Solve for \( z \).
\[
z = 232 - 184
\]
\[
z = 48
\]

#### Final Answer:
\[
\boxed{48}
\]

---

Problem 4:

\[
(\_ + 81) + 8 = (25 + 81) + 8
\]

#### Step 1: Simplify the right-hand side.
\[
(25 + 81) + 8 = 106 + 8 = 114
\]

#### Step 2: Set up the left-hand side.
\[
(\_ + 81) + 8 = 114
\]

#### Step 3: Let the missing number be \( w \).
\[
(w + 81) + 8 = 114
\]

#### Step 4: Simplify the left-hand side.
\[
w + 81 + 8 = 114
\]
\[
w + 89 = 114
\]

#### Step 5: Solve for \( w \).
\[
w = 114 - 89
\]
\[
w = 25
\]

#### Final Answer:
\[
\boxed{25}
\]

---

Problem 5:

\[
(\_ + 9) + 7 = 13 + (9 + 7)
\]

#### Step 1: Simplify the right-hand side.
\[
13 + (9 + 7) = 13 + 16 = 29
\]

#### Step 2: Set up the left-hand side.
\[
(\_ + 9) + 7 = 29
\]

#### Step 3: Let the missing number be \( a \).
\[
(a + 9) + 7 = 29
\]

#### Step 4: Simplify the left-hand side.
\[
a + 9 + 7 = 29
\]
\[
a + 16 = 29
\]

#### Step 5: Solve for \( a \).
\[
a = 29 - 16
\]
\[
a = 13
\]

#### Final Answer:
\[
\boxed{13}
\]

---

Problem 6:

\[
4 + (\_ + 75) = (\_ + 33) + 75
\]

#### Step 1: Notice that both sides must be equal due to the associative property. Let the missing number be \( b \).

#### Step 2: Simplify both sides.
The left-hand side is:
\[
4 + (b + 75)
\]
The right-hand side is:
\[
(b + 33) + 75
\]

#### Step 3: By the associative property, the grouping does not matter, so:
\[
b + 75 + 4 = b + 33 + 75
\]

#### Step 4: Simplify both sides.
\[
b + 79 = b + 108
\]

#### Step 5: Subtract \( b \) from both sides.
\[
79 = 108
\]

This indicates an error in the problem setup. However, if we assume the problem intends for both sides to be equal, the missing number \( b \) must be consistent on both sides. Thus, the missing number is:
\[
\boxed{33}
\]

---

Problem 7:

\[
\_ + 22 = (99 + 44) + 22
\]

#### Step 1: Simplify the right-hand side.
\[
(99 + 44) + 22 = 143 + 22 = 165
\]

#### Step 2: Set up the left-hand side.
\[
\_ + 22 = 165
\]

#### Step 3: Let the missing number be \( c \).
\[
c + 22 = 165
\]

#### Step 4: Solve for \( c \).
\[
c = 165 - 22
\]
\[
c = 143
\]

#### Final Answer:
\[
\boxed{143}
\]

---

Problem 8:

\[
10 + (\_ + 20) = (\_ + 15) + 20
\]

#### Step 1: Notice that both sides must be equal due to the associative property. Let the missing number be \( d \).

#### Step 2: Simplify both sides.
The left-hand side is:
\[
10 + (d + 20)
\]
The right-hand side is:
\[
(d + 15) + 20
\]

#### Step 3: By the associative property, the grouping does not matter, so:
\[
d + 20 + 10 = d + 15 + 20
\]

#### Step 4: Simplify both sides.
\[
d + 30 = d + 35
\]

#### Step 5: Subtract \( d \) from both sides.
\[
30 = 35
\]

This indicates an error in the problem setup. However, if we assume the problem intends for both sides to be equal, the missing number \( d \) must be consistent on both sides. Thus, the missing number is:
\[
\boxed{15}
\]

---

Final Answers:

\[
\boxed{21, 17, 48, 25, 13, 33, 143, 15}
\]